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Chaolu, T. and Bai, Y.S. (2010) A New Algorithmic Theory for Determining and Classifying Classical and Non-Classical Symmetries of Partial Differential Equations. Scientia Sinica, 40, 331-348. (In Chinese)

has been cited by the following article:

• TITLE: Potential Symmetries, One-Dimensional Optimal System and Invariant Solutions of the Coupled Burgers’ Equations

  AUTHORS: Yuexing Bai, Sudao Bilige, Temuer Chaolu

  KEYWORDS: Potential Symmetry, One-Dimensional Optimal System, Invariant Solution, Coupled Burgers’ Equations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.9, September 11, 2018

  ABSTRACT: In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.